FR2801753A1 - Digital communications channel multiple channel equaliser technique having convergent recursive filter/transverse filter mode and output evaluator allowing second tracking mode switch where better results available. - Google Patents

Abstract

The digital communications system equaliser for several receivers forms transverse filters (9) for each reception channel. The convergent system has a forward recursive filter (8) on each reception channel feeding into a summer (10). There is a means of evaluating performance level, allowing a switch from normal operating mode to tracking mode or the inverse.

Description

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ADAPTIVE EQUALIZATION DEVICES FOR
RECEIVERS OF DIGITAL COMMUNICATION SYSTEMS
MULTI-CHANNEL PRESENTATION OF THE GENERAL DOMAIN OF THE INVENTION AND THE STATE OF THE TECHNIQUE
The present invention relates to the equalization device (or equalizer) for receivers of multi-channel digital communications systems.

 In current communications systems, the receivers include a number of functions including demodulation, ie baseband translation of the received signal, equalization, synchronization (timing and carrier), decision and channel decoding.

 Equalization, in its temporal version, essentially consists in reducing inter-symbol interference (IES), a phenomenon linked to the fact that, overall, the chain of communications does not satisfy what is known as the criterion of Nyquist. This can result from a poor filtering strategy, a wrong choice of the sampling time or a multipath propagation phenomenon. This is particularly the case on radio-mobile channels, ionospheric or tropospheric channels and on submarine acoustic channels.

 It is also recalled, for all practical purposes, that a communications system can be seen schematically as a source emitting, at a rate 1 / T and through an equivalent discrete channel, discrete symbols worth in an alphabet of finite dimension. This rate is called modulation rate and is expressed in Baud, T designating the time interval between the emission of two successive symbols.

 Historically, the first devices to fight the phenomenon of IES were introduced by Lucky in his publication:

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 [1] R. W. Lucky, Automatic Equalization for Digital Communications, BSTJ 44, pp. 547-588, April 1965.

 They were essentially synchronous linear transversal filters (using a single sample per symbol time) adaptive, the adaptivity being made necessary by the evolutionary nature of the transmission channel. The coefficients of the filter were updated according to a noise minimization criterion under zero IES stress (Zero Forcing in Anglo-American), this procedure leading to equalize the folded spectrum hence the terminology used.

 The schematic diagram of a transverse equalizer is illustrated in FIG. 1, on which a transfer function filter B (z) has been represented, as well as the decision circuit, referenced by 2, situated downstream of said filter 1. .

 It was only later that adaptive equalizers appeared, using as an optimality criterion the minimization of the mean square error (MSE). It turned out that, in the case of delicate channels, the cancellation of the IES could result in a significant increase in noise at the output of the equalizer thus contributing to a sharp deterioration in performance while On the other hand, the minimization criterion of the MSE proved to be a sensible compromise allowing a substantial reduction of the IES without significant increase of the noise.

 From a general point of view, adaptive equalization is conventionally done in two stages. During the first, the device is driven by a learning sequence, long enough to guarantee convergence, then, in the second step, it becomes auto-adaptive, that is to say that it is piloted from its own decisions, with all the risks inherent in this strategy.

 Later still, it was proposed in the publication: [2] CA Belfiore, JH Park, Feedback Equalization Decision, Proccedings of the IEEE 67 (8), August 79, non-linear recursive feedback decision equalizers (Decision Feedback Equalizer ), in which, as shown in Figure 2, the decided data is fed back into a rear filter 3, transfer function denoted A (z), constituting the recursive part of the equalizer.

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 This approach would make it possible to achieve performances that are much higher than those obtained by a linear equalizer. Unfortunately, these devices could, at the same time, prove to be extremely sensitive to decision errors, so much so that there was sometimes a phenomenon of propagation of errors that could lead to the divergence of the device whose output no longer relevant to the data that was issued.

 Under such conditions, it was then necessary to supervise the device periodically which resulted, at least, in a significant reduction in spectral efficiency.

 In other words, the behavior of the device had to be controlled periodically (or more permanently) so as to avoid a pathological functioning of the equalizer.

 A general object of the invention is to provide a technique for solving this problem in an elegant manner.

 From another point of view, if it is true that a decision feedback equalizer (DRE) is not optimal with regard to the criterion of minimization of the probability of error (equivalent to the criterion of maximum a posteriori) Nevertheless, the optimal receptor described in: [3] GD Forney, Jr, Maximum likehood sequence estimator of digital sequences in the presence of intersymbol interference IEEE Trans. On Information Theory, vol. IT-18n pp. 6363-378, May 1972, quickly becomes infeasible when the length of the impulse response is important. Indeed, such a device performs, at first, an estimate of the impulse response of the transmission channel and then search, among all the possible transmitted sequences, the one that would provide at the output of the channel thus estimated, the signal (vector) most close to the observation (vector) actually available.

 Currently, the implementation of such receivers requires the use of the Viterbi algorithm as described in: [4] G. D. Forney, Jr The Viterbi Algorithm, Proc. IEEE, vo1.61, pp.268-278, March 1973, the major interest of which is to allow decision-making along the water, without loss of optimality. in clear, it is not

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 necessary to have received the entire message to start making decisions on the most likely sequence of symbols.

 However, and by way of example, for a modulated signal with four phase states emitted through a discrete impulse response channel of length 15 (time spread of the order of 15 T), the trellis associated with a such a system has a billion possible states which makes, de facto, this type of receiver perfectly unrealizable, at least in the case of real-time applications. In a number of applications, such a time spread is common, such as underwater acoustic channels, ionospheric channels, telephone lines (twisted pairs) and this could, from a general point of view, be the the case of all transmission channels, if there were a significant increase in the bit rates in the allocated band.

 Indeed, we will obviously seek to carry more and more important flows on this type of channels, which will inevitably result in an extension of the temporal support of the impulse response. It is in this sense that the decision feedback equalizers constitute an interesting alternative to the optimal receivers when the discrete impulse response is of significant size. Thus, on the current GSM standard for radio-mobile communications, the time spread is of the order of 6T, which for a binary modulation represents 64 states and therefore lends itself well to the use of a reception technique optimal. If now, for obvious reasons of increase in online throughput, we move to a quaternary modulation and we seek parallel to increase the speed of modulation in a factor of 2, we end up with a number of states of 17 million, which is clearly prohibitive. It is for this reason that return-decision equalizers (DREs), although theoretically suboptimal, have a clear overriding interest in terms of complexity-performance trade-offs, provided, however, that their potentially pathological behavior is controlled.

 As already mentioned above, the method conventionally used on the severe channels consists in issuing a

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 periodic training sequence so that the ERD can be readjusted, if necessary. This is done to the detriment of the spectral efficiency which can then be strongly affected. This is the main reason for the existence of many current works in blind equalization (self-taught, unsupervised). The objective is to converge the device to its optimal solution, without the aid of learning sequences, ie, in this case, from the sole knowledge of the statistics of the signal emitted by the source . Several authors have, as such, made a significant contribution, among which: [5] Y. Sato, A method of self-recovering equalization for multilevel amplitude modulation, IEEE Trans. on Corn., COM-23, pp. 679-682, June 1975.

[6] D. N. Godard, Self-recovering equalization and carrier tracking in twodimensional data communication systems, IEEE Trans. on Com., COM-28, pp. 1867-1875, November 1980.

[7] A. Benveniste, M. Goursat, Blind equalizers, IEEE Trans. on Com., vol.32, 1984, pp. 871-883.

[8] O. Shalvi & E. Weinstein, New criteria for blind deconvolution of nonminimum phase systems (channels), IEEE Trans. IT, vol. 36, No. 2, March 1990, pp. 312-321.

[9] C.A. Da Rocha, O. Macchi and J.M.T. Romano, An adaptive nonlinear IIR filter for self-learning equalization, ITC 94, Rio de Janeiro, Brazil, pp. 6 to 10.1994.

[10] B. Porat, B. Friedlander, Blind Equalization of Digital Communication Channels, using high order "Trans.on SP, vol 39, pp. 522-526, Feb 1991.

[11] V. Shtrom & H. Fan, New Class of Zero-Forcing Cost Functions in Blind Equalization, IEEE Trans. SP, vol 46, N 10, October 1998, pp.

2674-2683.

 All these algorithms implicitly refer to statistics of order greater than two. This is related to the fact that a minimal phase channel requires, for its inversion, the use of such moments. The first ones

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 EQs of this type were generally linear and transverse, ie finite impulse response.

 Very recently, an elegant and particularly effective solution was introduced by Labat et al in: [12] J. Labat, C. Laot & O. Macchi, adaptive equalization device for digital communication systems, French patent 9510832 [13] J Labat, O. Macchi & C. Laot, Adaptive decision feedback equalization: Can you skip the training period? IEEE Trans. on Com., vol.46, No. 7, pp. 921-930, July 98.

 This new time equalizer, which is to be described description, comprises two modes of operation, adapted to the severity of the transmission channel. In the initial mode, called convergence mode and shown in FIG. 3, the device consists of the cascade of a purely recursive whitening filter 4, a transversal filter 5, an automatic gain control (AGC) 6 and a phase corrector 7.

The originality of the device is related to the fact that each stage is adapted according to a specific criterion, which confers on it both robustness and speed of convergence. When the equalization process is sufficiently advanced, which can be appreciated when considering the estimated mean squared error (MSE) (based on the decisions made by the receiver), the structure and adaptation criteria of the The equalizer is modified such that the device is transformed into a conventional decision feedback equalizer (ERD) (Figure 4). The reversibility of this change gives the new equalizer a substantial advantage in the sense that whenever it can, it takes advantage of its own decisions without risk of divergence, unlike conventional DREs. Indeed, if the transmission conditions suddenly change, the new equalizer resumes its initial configuration, which allows it to readjust to the new situation. In these conditions, the question of the choice between a linear device and an ERD type equalizer does not really need to be asked because this new equalizer is still able to choose the configuration that allows it to achieve the best performance.

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PRESENTATION OF THE INVENTION
An object of the invention is to provide a multi-channel equalizer, especially spatio-temporal (that is to say an equalizer able to exploit the signals simultaneously detected by several sensors in parallel), which is particularly powerful.

 For this purpose, the invention proposes an equalization device for digital reception multi-channel communication systems which, in normal operation, has a structure which comprises transverse filter means for each of the reception channels, means for summation. different channels, as well as a chain which is downstream of said summing means and which comprises phase correction means, as well as decision means and a purely recursive filter, characterized in that in a convergence mode and / or or difficult reception, it has a structure that includes a purely recursive filter on each of the reception channels, the purely recursive filter being removed from the chain downstream of the summing means, the device comprising means for evaluating its degree of performance in function of the output signal of said device and to, depending on the result of this evaluation, switch from the struct ure which corresponds to the normal operating mode, also called mode of continuation or easy receptions, to the structure which corresponds to the operating mode of convergence or difficult receptions or reciprocally.

 Such a device is advantageously completed by the following different characteristics taken alone or according to their technically possible combinations: it comprises means for modifying the criteria for updating the transverse and recursive parts that the device operates in normal mode or in convergence mode or difficult receptions.

- In convergence mode or difficult receptions, the recursive filters are updated according to a quadratic criterion, the transverse filters being updated according to a statistical criterion of order greater than two.

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it comprises means for driving it, in tracking mode or easy receptions, so as to minimize the estimated mean squared error.

- the degree of performance is determined based on an estimate of the mean squared error.

in the convergence mode, the phase correction means are arranged in the immediate vicinity of the decision means.

it comprises automatic gain control means.

- In tracking mode or easy receptions, the automatic gain control means are constituted by the transverse filter means - in convergence mode, the automatic gain control means is located upstream of the recursive filters.

 The invention also relates to a split-type equalization device, in which the received data are distributed by fractionation over several channels, characterized in that it consists of a device of the aforementioned type.

 It also relates to a continuous data transmission system or a packet data transmission system, characterized in that it comprises an equalization device of the aforementioned type.

 Such a spatio-temporal equalizer is self-learning with decision feedback and variable configuration. According to a signal developed in line such as the estimated mean squared error, or the kurtosis of the output signal of the equalizer or, more generally, any relevant cost function (Godard [6], Shalvi & Weinstein [8], Shtrom & Fan [11], ...), the equalizer is optimally configured, in terms of structure and optimality criteria. In its initial mode of operation, called the convergence mode, the device is linear and recursive whereas, in its normal mode of operation, called the tracking mode, this device becomes the classic spatio-temporal ERD driven by its own decisions. The transition from one to the other of these two configurations is perfectly reversible, which makes it particularly attractive in the case of non-stationary channels. As a result, the device proposed by the invention makes it possible

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 to achieve very interesting performances in terms of both convergence and prosecution. This essential property allows it to adapt to the fluctuations of the channel in severe situations, unlike classical equalizers of the prior art. From this point of view, the device proposed by the invention is particularly well suited to non-stationary channels such as radiomobile, ionospheric, tropospheric and acoustic channels underwater.

PRESENTATION OF FIGURES
Other features and advantages of the invention will become apparent from the description which follows. This description is purely illustrative and not limiting. It should be read with reference to the accompanying drawings in which: - Figure 1 is a block diagram of a temporal transverse linear equalizer.

 FIG. 2 is a block diagram of a time decision feedback equalizer.

 FIG. 3 is a diagram which illustrates the structure, in convergence mode, of a previously proposed temporal equalizer [12].

 FIG. 4 is a diagram illustrating the structure, in tracking mode, of the same time equalizer.

 FIG. 5 is a diagram illustrating the structure, in convergence mode, of a spatio-temporal equalizer in accordance with one possible embodiment for the invention.

 FIG. 6 is a diagram illustrating the structure, in tracking mode, of a spatio-temporal equalizer according to one possible embodiment for the invention.

 FIG. 7 is a diagram illustrating the structure, in convergence mode, of a fractional spatio-temporal equalizer in accordance with one possible embodiment for the invention.

 FIG. 8 is a diagram illustrating the structure, in convergence mode, of a fractional spatio-temporal equalizer in accordance with one possible embodiment for the invention.

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 FIGS. 9 to 11 are graphs on which quadratic mean error, correlator output and input and output constellation curves have respectively been reported in the case of a synchronous driven decision feedback equalizer. , for one, two and four reception channels.

 FIGS. 12 to 14 are graphs on which quadratic mean error, correlator output and input and output constellation curves have respectively been reported in the case of a synchronous self-learning decision feedback equalizer , for one, two and four reception channels.

 FIGS. 15 to 17 are graphs on which mean squared error, correlator output curves and input and output constellations have respectively been reported in the case of a fractionally trained decision feedback equalizer. , for one, two and four reception channels.

 FIGS. 18 to 20 are graphs on which quadratic mean error, correlator output and input and output constellation curves respectively have been plotted in the case of a fractional self-learning decision equalizer. , for one, two and four reception channels.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION
GENERAL PRESENTATION
The multi-channel equalization device proposed by the invention has two different structures depending on whether one is in convergence mode (mode 1) or tracking mode (mode 2), ie in operating mode normal. These two structures are illustrated in Figures 5 and 6.

 In the structure used during the convergence mode (FIG. 5), a purely recursive filter 8 precedes a transversal filter 9 on each of the P channels used by the space-time equalizer. Further downstream, after the adder 10, there is respectively an automatic gain control

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 11 and a phase corrector 12. All these elements are adapted from blind criteria, that is to say not involving the knowledge of the transmitted data but simply a priori knowledge of their statistical properties.

 In the tracking mode, the place of the transverse and recursive filters is modified so that the device is configured in conventional spatio-temporal ERD (FIG. 6). The global optimality criterion then becomes that of the minimization of the estimated mean squared error (MSE). In this mode of operation, the AGC is generally inhibited, ie locked at the value prior to the structural change. At the same time, there is a structural change and a change in optimality criteria. Thus, depending on the degree of severity of the channel and from a signal developed online, which measures the performance of the device such as, for example, the quadratic error, or kurtosis (cumulative order 4) of the output signal w (k), all other estimated online cost function (Godard [6], Shalvi & Weinstein [8], Shtrom and Fan [11], ..), the device switches from a self-learning recursive linear structure as illustrated on Figure 5 to a spatio-temporal non-linear ERD structure as shown in Figure 6 or, conversely, a decision-driven ERD type structure to a self-taught linear recursive structure. The corresponding structures on the one hand in convergence mode and on the other hand in continuation mode will now be described.

 Naturally, in its mode of convergence, the device being linear, the place of the different elements constituting the spatio-temporal ERD can be modified. This modification concerns in particular the AGC which can be placed in several places of the chain and even possibly deleted (which amounts to making g = 1), the transverse filters being then responsible for performing this function. Thus, illustrative but not limiting, the AGC may be located directly upstream or downstream of the phase corrector, or upstream or downstream of the purely recursive filter. With regard to the phase corrector responsible for carrying out the carrier recovery operation according to the

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 Anglo-Saxon terminology), although from a theoretical point of view it may be located at any point in the chain, it is clear that its ideal position lies in the immediate vicinity of the decision-making circuit. This is related to the criterion generally used for adaptation, namely the minimization of the estimated mean squared error. Nevertheless, other more robust criteria using current art techniques can also be used.

 1) Mode 1: convergence mode and / or difficult reception periods.

 The structure corresponding to the convergence configuration illustrated in FIG. 5 comprises on each of the P channels corresponding to the P sensors of the antenna a purely recursive filter 8, identical on each channel, of transfer function 1 / [1 + A (z )], transverse filters 9 of transfer function B, (z), i = 1, 2, .., P, of an adder 10, of an automatic gain control device 11 and of a phase corrector 12.

 The respective place of the AGC and the phase corrector (carrier recovery) has theoretically no theoretical importance, at least in a non-adaptive strategy. Thus the AGC (characterized by g) can be located upstream or downstream purely recursive filters or upstream or downstream of the phase correction device, or deleted. One position among others is that illustrated in Figure 5.

 The gain g of the device 11 is updated according to a blind criterion, the recursive filters on a quadratic criterion and the transverse filters on a criterion involving statistics of order greater than two. For the updating of the coefficients of the transversal filters, several algorithms can be used and in particular those of Godard [6], Shalvi & Weinstein [8], Shtrom & Fan [11], etc.

 Carrier recovery or phase correction, that is to say the estimation of the phase error and its compensation in the form of a complex multiplication by exp (-j <9), is carried out for example according to a criterion minimization of estimated mean squared error. The error signal

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 elaborated can then be filtered so as to fall back on a device of the second order (or order greater than 2 if necessary). This device can also be located at various points in the chain because of the linearity of the device. Nevertheless, in practice, at least for the criterion considered, it seems advisable to situate it downstream of the equalizer. In this mode of convergence, the phase correction can be controlled by decisions, although other more robust criteria exploiting the symmetry of the constellation of the transmitted signal can be envisaged. In any case, the other functions are optimized based on criteria that do not rely on the decisions made by the appropriate device (threshold circuit). This first step is, therefore, perfectly self-taught (blind, unsupervised). In addition, each of the elementary devices has an appropriate criterion of optimality, which gives the set a very robust character.

 2) Mode 2: Tracking and / or easy receiving periods.

 Since the channel is practically equalized, which can be deduced from the observation of the estimated MSE, kurtosis, or any other cost function (Godard [6], Shalvi & Weinstein [8], Shtrom & Fan [11], ..), the purely recursive linear function transfer filters 1 / [1 + A (z)], are replaced by a single filter of the same transfer function 13 which undergoes the change of position indicated on FIG. Figure 6 and which is now powered by the decisions # (k) taken by the decision circuit, referenced 14, the device. The factorization of this function obviously requires having, in the convergence mode 1, an identical recursive filter on the P lanes of the space-time ERD. The new structure obtained is that of the conventional spatio-temporal ERD, driven by decisions, according to the criterion of minimization of the estimated mean squared error. Moreover, if the decided data is judged to be of low likelihood, then it is possible to choose to reinject the signal w (k) at the input of the decision circuit into the filter A (z), in place of the data decided on ( k).

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 Indeed, it is considered that it is better, punctually, to inject noisy data w (k) into the recursive filter A (z) than to make the risk of injecting a decided datum d (k) of low likelihood (thus probably erroneous). This way of proceeding is likely to make the device more robust in mode of continuation and constitutes, as such, a potential improvement of the spatio-temporal ERD). Furthermore, in this tracking mode, the AGC can be integrated in the transverse filters B, (z) by blocking g to its previous value.

 Thus, as will be understood, the space-time equalizer has two different modes of operation associated with different structures and optimality criteria.

 One of the essential features of the new device is that this structural change is perfectly reversible. Such a property is interesting and allows, in case of severe situations, to return to the mode of convergence, that is to say a very robust mode of operation. On the other hand, as soon as the severity of the channel decreases, this results in a decrease in the associated mean squared error, and the system then switches back to tracking mode, that is to say towards a structure of equalizer to return decisions and so on. In this the device has an original character and particularly attractive.

 In parallel with this structural permutation, a change of criteria is necessary to update the coefficients of the transverse and recursive parts. In mode 1, these criteria are based exclusively on the prior knowledge of the statistics of the signal emitted by the source while in the tracking mode, the criterion of optimality is that of the minimization of the estimated MSE.

DETAILED DESCRIPTION OF AN EXEMPLARY EMBODIMENT
We will now describe in detail an embodiment of the spatio-temporal equalization device object of the invention.

1) Convergence mode and / or difficult reception periods.

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 1-1 Equations of operation.

u, (k) = s, (k) a, u, (k - 1) = s, (k) - A 'U,,,v (k) 1-1 l=1 où s, (k) désignele signal en entrée de la voie i au temps k, u, (k) désignele signal en sortie du filtre 8 de la voie i, et où A=[a1, a2, ..., aN]T I-2 U@,N(k)=(ui(k-1), u,(k-2), ..., u,(k-N))T I-3 On a également : v,(k)= #bi,lui(k-l) = BiTUi,L+1(k) I-4 l=0 où v, (k) désignele signal en sortie du filtre transverse 9 de la voie i et où
Ui,L+1 (k) = (u, (k), ui(k-1),..., u, (k - L))T I-5 Bi=Bi,0,bi,l, ..., bi,L]T I-6 On a en outre : v (k) = #vi(k) I-7 w(k) = v(k)g(k -1) exp[-j#(k-1)] 1-8 A titre d'exemple les vecteurs B, peuvent être initialisés avec B,(0)=[0, 0, 1/P, 0, 0]T tandis que C(0) est le vecteur nul de dimension N. The equations that govern the operation of the device are as follows: For i = 1, 2, .., P, we have:

u, (k) = s, (k) a, u, (k - 1) = s, (k) - A 'U ,,, v (k) 1-1 l = 1 where s, (k) denoted signal at the input of the channel i at the time k, u, (k) designates the signal at the output of the filter 8 of the channel i, and where A = [a1, a2, ..., aN] T I-2 U @, N (k) = (ui (k-1), u, (k-2), ..., u, (kN)) T I-3 We also have: v, (k) = # bi, it ( kl) = BiTUi, L + 1 (k) I-4 l = 0 where v, (k) designates the signal at the output of the transverse filter 9 of the channel i and where
Ui, L + 1 (k) = (u, (k), ui (k-1), ..., u, (k-L)) T I-5 Bi = Bi, O, bi, l,. .., bi, L] T I-6 We have: v (k) = #vi (k) I-7 w (k) = v (k) g (k -1) exp [-j # (k -1)] 1-8 For example the vectors B, can be initialized with B, (0) = [0, 0, 1 / P, 0, 0] T while C (0) is the null vector of dimension N.

 1-2 Update of parameters in convergence mode.

1-2-1 Purely recursive filter
The optimization criterion used for the adaptation of the recursive filter is the minimization of the cost function:

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This can be done using a stochastic gradient algorithm or recursive least squares technique. We give here the discounting equation derived from the stochastic gradient algorithm: AT (k) = AT (k -1) + a # ui (k) Ui, N * (k) I-10 With! -La an appropriate adaptation step.

1-2-3 Transverse filters.

v(k) ~ v, (k) = BT (k -l)U(k) 1-11 Avec BT = [B1@,B2T,...,BPT] 1-12 UT (k) - [U1,L+1T (k), U2,L+1T (k),..., UP,L+1T (k)] I-13
Les critères utilisés pour l'actualisation sont, de manière non limitative, ceux de Godard [6], de Shalvi & Weinstein [8] ou de Shtrom et Fan [11 ]. A titre purement indicatif, on rappelle que la fonction coût définie par Godard est la suivante :

The signal v (k) can be written in a more concise way:

v (k) ~ v, (k) = BT (k-1) U (k) 1-11 With BT = [B1 @, B2T, ..., BPT] 1-12 UT (k) - [U1, L + 1T (k), U2, L + 1T (k), ..., UP, L + 1T (k)] I-13
The criteria used for updating are, without limitation, those of Godard [6], Shalvi & Weinstein [8] or Shtrom and Fan [11]. For purely indicative purposes, it is recalled that the cost function defined by Godard is as follows:

Jsw (B) = Ew(k)I4 ? avec la contrainte E{v(k)12}= cr3 1-15
Shtrom et Fan ont proposé un certain nombre de fonctions coûts pouvant également être utilisées pour l'actualisation des filtres transverses et qui sont parfaitement décrites dans [11]. D'une manière générale, les algorithmes qui découlent de ces critères ont été décrits dans les articles In practice the parameter p is chosen equal to 2 but other values are also possible. The criterion proposed by Shalvi & Weinstein is as follows:

Jsw (B) = Ew (k) I4? with the constraint E {v (k) 12} = cr3 1-15
Shtrom and Fan have proposed a number of cost functions that can also be used to update transverse filters and which are perfectly described in [11]. In general, the algorithms that derive from these criteria have been described in the articles

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Avec b un pas d'adaptation approprié. referenced, at least in their stochastic gradient version. For purely illustrative purposes, we recall the update relation resulting from the Godard algorithm (p = 2):

With b no appropriate adaptation.

 As already mentioned, and for purely indicative purposes, the reference coefficient can be chosen equal to 1 / P for each of the filters B ,, while its position is left free. In practice, the position of these coefficients, which conditions the delay of restitution of the equalizer, is chosen so that these filters are rather anticausal tendency.

1-2-4 Phase Correction.

L'algorithme d'actualisation qui en découle est le suivant :

Avec # un pas d'adaptation approprié. One possible criterion is the minimization of the estimated MSE (from the decided data). This criterion is then clearly driven by decisions, so less robust, hence the position of the device downstream of the chain, so as not to disturb the upstream stages. The cost function then has for expression:

The resulting update algorithm is as follows:

With # a suitable adaptation step.

1-2-5 Automatic gain control.

 Although the gain control device is not essential, it may be interesting, in some cases, to predict it. Again, given the linearity of the structure, the position of this device can be chosen arbitrarily. One position among others is that

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Avec G(0)=1 et g un pas d'adaptation approprié tandis que #d2 désigne la variance des données émises par la source. represented in FIG. 5. In this case, a possible algorithm for updating the gain g corresponds to the following discounting equation:

With G (0) = 1 and g an appropriate adaptation step while # d2 denotes the variance of the data emitted by the source.

2- Règle de commutation. An equally interesting solution, in terms of stability, is to situate the AGC, characterized by g, upstream of the purely recursive transfer function filters 1 / [1 + A (z)]. A possible algorithm for updating the gain g corresponds to the following discount equation:

2- Switching rule.

ou toute autre fonction coût élaborée selon le même principe, par exemple et pour illustrer le propos, celle de Godard [6] estimée selon :

Où # désigne un facteur d'oubli. To control the current operating mode (convergence or tracking), a signal to evaluate the degree of performance of the equalizer is developed online. For this, one can, for example, determine the estimated MSE MDD (k) according to the algorithm:

or any other function cost developed according to the same principle, for example and to illustrate the subject, that of Godard [6] estimated according to:

Where # is a forgetting factor.

{M IJIJ (k0 ) > Mo mod e de convergence si k > ko 1-25 M"" (ka ) < Mo mod e de poursuite si k > ko In the case where the estimated MSE is used as a control signal, the choice of the configuration is then made according to the following algorithm:

{M IJIJ (k0)> Convergence model if k> ko 1-25 M "" (ka) <Continuation model if k> ko

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Clearly, when the estimated EQM MDD (k) is greater than a threshold Mo, the equalizer is in convergence mode while on the contrary when it is less than Mo, it is in tracking mode.

 It is observed that in this case the estimated MSE is then very close to the true MSE. To ensure a safe transition in ERD mode, the threshold must be chosen small enough. In addition, in general, when the MSE decreases the probability of error also decreases. It is therefore necessary to determine a threshold corresponding to a sufficiently low BER, typically of the order of 0.02 to avoid pathological behavior of the equalizer. If we consider that in its mode of convergence the equalizer is of type Zero-Forcing, the BER can express itself according to the MSE. thus, for a 4-QAM, such a constraint leads to choose a threshold Mo = 0.25 (-6 dB). Note that, in this case, the estimated MSE is generally very close to the true MSE and therefore, as such, is a good performance index for controlling the operating mode of the equalizer.

3-Mode of pursuit and / or easy reception periods.

 This operating mode begins when a signal developed online such as the estimated MSE crosses a threshold adapted to the modulation used (for example 0. 25 for the MDP4). In this case, the position of the transversal filters and the recursive filter is rotated to obtain the conventional spatio-temporal ERD. Clearly, the equalizer goes from a linear recursive structure to a non-linear recursive structure and vice versa depending on the severity of the context. In this mode of operation the criterion is then unique, namely the minimization of the estimated MSE. This criterion is used to update all the parameters of the equalizer, from a stochastic gradient algorithm or recursive least squares (Recursive Least Square) or any other algorithm corresponding to the current state of the art . The automatic gain control characterized by g is generally blocked at its previous value, this function then being automatically performed by the different transverse filters. In contrast, the phase corrector

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 is maintained, but its position can also be modified according to the diagram of Figure 6.

 3-1 Equations of operation.

B, (k) = B, (k -1) +,ub g(k -1) exp( j B(k -1))ld (k) - w(k)S; (k) i =1,2,..., P I I-5 3-2-3 Filtre récursif A1 (k) = A' (k-1)- a##(k)-w(k)#D*(k) II-6 3-2-4 Correcteur de phase
L'algorithme d'actualisation est le suivant : The equations that govern this mode of operation are: p (k) = g (k -1) exp (-j # (k-1)) # BiT (k-1) Si (k) 11-1 With Si ( k) = (if (k), if (k-1), ..., if (kL)) T 11-2 and w (k) = p (k) -At (k-1) D (k) 11-3 With D (k) = (# (k-1), # (k-2), ..., # (kN)) 7 11-4
3-2 Updating parameters in tracking mode 3-2-1 Cross-section filters
The updating equations of the filters B, (z) of the spatial-temporal equalizer are then:

B, (k) = B, (k -1) +, ub g (k -1) exp (j B (k -1)) 1d (k) - w (k) S; (k) i = 1,2, ..., PI I-5 3-2-3 Recursive filter A1 (k) = A '(k-1) - a ## (k) -w (k) # D * (k) II-6 3-2-4 Phase Corrector
The update algorithm is as follows:

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#(k) = #(k-1) + #e(k) 11-9 Avec # un pas d'adaptation approprié.

# (k) = # (k-1) + #e (k) 11-9 With # a suitable adaptation step.

 Particular case.

It is important to note that in the case of two-state phase shift (Binary Phase Shift Keying), the optimal quadratic criterion is the minimization of the following cost function: EQMmdp2 = E {[ Re {w (k) - # (k)}] 2}
The resulting equations are then deduced directly, without any particular problem. For CDM2, this criterion is the most relevant of the quadratic criteria. In addition, in the convergence mode, the relevant criterion for the adaptation of the vector A of the recursive filter is the minimization of the following cost function:

Subject to constrain the coefficients of the vector to be real.

The resulting equations are obtained directly. The other criteria are in all respects similar to the previous except for the phase correction that uses the minimization of the EQMmdP2.

 In the foregoing, the two modes of operation of an autodidactic space-time ERD in accordance with a possible embodiment of the invention have been described. Previously developed actualizations are derived from the stochastic gradient algorithm. Naturally, they can also be obtained by a technique of least squares, fast least squares or any other technique corresponding to the current state of the art.

 The level of performance achieved by this device is remarkable because in case of degradation of the channel, the device is then configured

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 automatically in the convergence mode. On the contrary, as soon as the channel improves, which is detected from an on-line signal, our device configures itself in tracking mode and so on.

 Finally, the principle of the equalizer which has just been presented, which is the subject of the invention, can extend to fractional equalizers (fractional equalizers), ie using samples temporally spaced by a duration elementary lower than T, for example T / 2.

Such a device is perfectly described by the diagrams of Figures 7 and 8. For this, considering a fractional equalizer using samples taken at a rate 2 / T, which corresponds to a very common practice, we define the signals s, j (k) as follows: S1,1 (k) = s1 (kT) S1,2 (k) = s1 [kT-T / 2] Sp, 1 (k) = sp [kT] Sp, 2 (k ) = sp [kT-T / 2]
For the other signals appearing in FIGS. 7 and 8, the same principle has been adopted as regards the notation.

 In its mode of pursuit the updating equations are those of the conventional fractional ERD corresponding to the state of the art. as far as the convergence mode is concerned, it suffices to consider the intermediate samples sn, 2 (k) = sn [kT-T / 2] as emanating from a second sensor and therefore the preceding equations fully apply to the new device that can, from a general point of view, be seen as a spatio-temporal ERD to 2P sensors.

APPLICATIONS
The previously described device is directly applicable to continuous stream data communications systems as well as packet mode transmission systems (blocks, bursts, bursts). For this last mode of transmission, it is enough to repeat the process of equalization of the block as many times as necessary. The basic idea is then very simple.

One operates a first pass on the considered block (packet). In these

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 conditions, the parameters (of the equalizer) estimated at the end of this pass are then closer to their final values. So, the next iteration is done by initializing the device parameters by the estimated values at the end of the previous iteration and so on. By operating a certain number of passes, typically 4 or 5, we arrive at a very exceptional result. This procedure makes it possible to work on packet transmission systems and, by way of example, for an MDP2 modulation, the minimum block size required for this blind strategy is of the order of 150 symbols, which is extremely interesting and meets the requirements imposed by current standards. This procedure is very interesting in terms of application, since many current systems use time-division multiple access.

 The fields covered by this invention are, but not limited to, Hertzian, radiomobile, tropospheric, ionospheric and underwater acoustic telecommunications. These delicate channels all have the specificity of being strongly non-stationary and generally display long pulse responses with respect to the symbol time T, prohibiting de facto the use of optimal receptors as described by G.D. Forney [3]. Similarly, the cables or telephone pairs may also be concerned by the device object of the invention. it suffices to choose P = 1 (a single sensor) and to opt for a split strategy: the device can in this case be likened to a spatio-temporal ERD with two sensors. Current projects for broadband transmission over twisted pairs (XDSL, HDSL, VDSL, etc.) are potential applications for this new device.

 The types of modulations concerned by this invention are all linear modulations and in particular amplitude modulations (Pulse Amplitude Modulation), amplitude modulations according to two carriers in quadrature (QAM), phase modulations (MDP-M) as well as as certain frequency modulations (GMSK, etc.). Overall, the new device can adapt to almost all modulations currently used.

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 Already, this new equalizer has been successfully tested on underwater acoustic communications signals. The results are really convincing, even for packet mode transmissions. It is clear that in the current scientific community, blind treatments are often unfairly considered as promising techniques but require a prohibitive convergence time with regard to current packet transmission applications. In fact, the space-time equalizer object of the invention makes it possible to obtain extremely interesting performances on blocks of modest size. To illustrate the point, in the context of undersea acoustic communications (ASM), we have successfully processed blocks of 1000 symbols of a four-phase modulated signal (QPSK or QPSK in English), debit 25 kbit / s, while the time support of the impulse response was spread over nearly 60T, which is huge. There is no doubt that such results are likely to modify certain practices, particularly in the field of ASM communications where the quantities of information exchanged are sometimes small. In these applications, currently implemented techniques generally use non-coherent receivers while it is perfectly possible to consider coherent reception techniques, and therefore more efficient, using a transmission in packet mode. Naturally, the duration of the packet must be chosen so that, on this horizon, the transmission channel can be considered as stationary.

 EXAMPLE OF APPLICA TION.

 To illustrate the performance of the new device, some results obtained in ASM communications are compared below by a conventional spatio-temporal trained equalizer and with a spatio-temporal equalizer of the type just described. The modulation used is of type MDP4 (QPSK in Anglo-American), the carrier frequency of 62 kHz and the digital bit rate of 33 kbit / s. the answer

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 discrete impulse of the transmission channel has a temporal support of the order of 60 T, which in fact prohibits any optimal reception technique in the sense of maximum likelihood.

 As regards the space-time equalizer, synchronous and fractional strategies are studied at all, in both the driven and blind modes. the training sequence comprises 1000 symbols. The various graphs describe in particular the evolution of the estimated MSE from the decided data. At the same time, the signal obtained by passing the decided data d (k) in the correlator corresponding to the transmitted sequence (white sequence of maximum length comprising 2047 symbols) in the case of 1.2 or 4 sensors is indicated in each case. .

Finally, the third type of graphs describes the input and output constellations of equalizers with respectively 1.2 or 4 sensors.

 The results are shown in Figures 9 to 20. It appears through these figures that the blind solution outperforms very clearly the driven solution, whether in synchronous version or fractional version.

 Even in its 4-sensor split version (Figure 16), the trained spatio-temporal equalizer fails to cope. On the other hand, from a single sensor, the output of the fractional blind equalizer starts to become relevant (FIG. 19) as evidenced by the presence of the peaks at the output of the correlator, peaks which reflect the recognition of the transmitted message .

 This trend is sharply accentuated with two sensors and is confirmed more clearly with four sensors.

 Thus, through these few results on a real data file, it appears that the spatio-temporal ERD object of the invention is an innovative technique displaying very interesting performance on a most severe transmission channel.

Claims (12)

1. Equalization device for digital reception multi-channel communication systems, which has in normal operation a structure which comprises transverse filter means for each of the reception channels, means for summing the different channels, as well as a chain which is downstream from said summing means and which comprises phase correction means, as well as decision means and a purely recursive filter, characterized in that in a difficult mode of convergence and / or reception, it presents a structure which comprises a purely recursive filter on each of the reception channels, the purely recursive filter being removed from the chain downstream of the summing means, the device comprising means for evaluating its degree of performance as a function of the output signal of said device and to, depending on the result of this evaluation, switch from the structure that corresponds to the mode of fon normal operation, also called tracking mode or easy receptions, to the structure that corresponds to the operating mode of convergence or difficult receptions or reciprocally.  2. Device according to claim 1, characterized in that it comprises means for modifying the criteria for updating the transverse and recursive parts that the device operates in normal mode or in convergence mode or difficult receptions.  3. Device according to claim 2, characterized in that in convergence mode or difficult receptions, the recursive filters are updated according to a quadratic criterion, the transverse filters being updated according to a statistical criterion of order greater than two.  4. Device according to one of claims 2 or 3, characterized in that it comprises means for driving, tracking mode or easy receptions, so as to minimize the estimated mean squared error. <Desc / Clms Page number 27>  5. Device according to one of the preceding claims, characterized in that the degree of performance is determined according to an estimate of the mean squared error.  6. Device according to one of the preceding claims, characterized in that in convergence mode, the phase correction means are arranged in the immediate vicinity of the decision means.  7. Device according to one of the preceding claims, characterized in that it comprises automatic gain control means.  8. Device according to claim 7, characterized in that in tracking mode or easy receptions, automatic gain control means are constituted by means forming transverse filters 9. Device according to claim 7, characterized in that in convergence mode, the automatic gain control means is located upstream of the recursive filters.  10. Fractional equalization device, wherein the received data are distributed by fractionation over several channels, characterized in that it consists of a device according to one of the preceding claims.  11. Continuous data transmission system, characterized in that it comprises an equalization device according to one of claims 1 to 10.  12. A packet data transmission system, characterized in that it comprises an equalization device according to one of claims 1 to 10.